Many medical conditions, including heart disease, can lead to a loss of blood flow to certain tissues, which can impair the cells' ability to maintai an appropriate concentration of hydrogen ions (protons) inside. This microscopic failure can cascade towards heart failure, stroke, and death, making it crucial to understand how proton concentration (a quantity measured in pH) affects the behavior of different proteins in the cell. An excellent example of pH's importance in human life may be found in the protein hemoglobin, which carries oxygen through the blood. The chemical byproduct of muscle exertion (for example, during exercise) is a lowered pH near the muscle, which causes hemoglobin to release more of its oxygen just where it is needed. We have a new theory that predicts how protein function depends on pH, and initial results suggest that the new theory may be an accurate model of pH dependence of proteins. In contrast, many existing models exhibit unexplained weaknesses that have not been resolved despite intense research. In this project, we will test the new theory on proteins that have been experimentally studied in great detail, and compare the new theory's predictions to those from existing models. The new approach, called nonlocal electrostatics, is an example of a multiscale model because it captures physics that are important at very small length scales (say, the size of a water molecule) as well as those that are important at much larger length scales (the size of a large protein). Although this multiscale theory has been known by physicists for almost forty years, the difficulties of testing the theory on biologically meaningful problems kept it from being applied until just a few years ago. Even then, computer speed and memory limitations prevented the study of large molecules; the investigator has recently developed a fast computer simulator, which makes the proposed protein simulations feasible for the first time. The investigator has conducted a preliminary study that suggested the new theory holds the promise of explaining several important and unresolved questions in protein physics, including pH dependence; here, we will study actual proteins, abandoning the simplifications in the preliminary work. Our first aim is to answer several fundamental questions about the new nonlocal electrostatic model, and its relationship to well known theories. Is nonlocal theory more accurate for all molecules, or are there special types of molecular shapes where it is not better? To address these questions, we must conduct systematic calculations, using a new strategy for comparison that we have developed in earlier work. In addition to teaching us about the new nonlocal theory, these calculations will also provide new insights into the popular existing ones. The second aim of this work is to compute actual pH-dependent properties of real proteins, focusing on those for which the most experimental data is available. To ensure scientific reproducibility and advance the field of pH simulations, our computer software will be released as open-source software and data files will be shared freely via the internet.